Speaker: Hengyu Zhou (Chongqing University)
Time: 14:00-15:00, Sep 15, 2022
Room: Tencent Meeting: 815-811-132, no password
In this paper we characterize the L^1 convergence of C^2 bounded functions such that their graphs have uniformly bounded mean curvature. As an application with Gerhardt's approximate process, we established the existence of closed or C^｛3，alpha｝ compact prescribed mean curvature (PMC) hypersurfaces in conformally product manifolds with its mean curvature equal to a C^｛1，alpha｝ function under a natural barrier condition. Moreover, these hypersurfaces are homeomorphic to the underlying n-dimensional Riemannian manifold for 2=<n=<7. In addition, if a quasi-decreasing condition of PMC functions is satisfied, such PMC hypersurfaces are C^1 graphs.
